It is well-known that mechanical disturbances can be used to generate elastic waves in earth formations surrounding a borehole, and the properties of these waves can be measured to obtain important information about the formations through which the waves have propagated. Parameters of compressional, shear and Stoneley waves, such as their velocity (or its reciprocal, slowness, which corresponds to the interval transit time typically measured by sonic logging tools) in the formations and in the borehole, can be indicators of formation characteristics that help in evaluation of the location and/or producibility of hydrocarbon resources. A sonic tool (or acoustic tool, logging device, etc.) can be used to obtain and analyze sonic logging measurements of formations surrounding an earth borehole. A sonic tool can include one or more acoustic sources and one or more acoustic receivers. An example sonic tool is SONIC SCANNER™ of SCHLUMBERGER LIMITED. In conventional use of a sonic tool, one can obtain compressional slowness, DTc, shear slowness, DTs, and Stoneley slowness, DTsh, each as a function of depth, z.
An acoustic source in a fluid-filled borehole generates head waves as well as relatively stronger borehole-guided modes. A standard sonic measurement system includes, for example, placing a piezoelectric source and an array of hydrophone receivers inside a fluid-filled borehole. The piezoelectric source can be configured in the form of either a monopole source or a dipole source. The source bandwidth typically ranges from 0.5 to 20 kHz. A monopole source generates primarily the lowest-order axisymmetric mode, also referred to as the Stoneley mode, together with compressional and shear head waves. In contrast, a dipole source primarily excites the lowest-order flexural borehole mode together with compressional and shear head waves. The head waves are caused by the coupling of the transmitted acoustic energy to plane waves in the formation that propagate along the borehole axis.
An incident compressional wave in the borehole fluid produces critically refracted compressional waves in the formation. Those refracted along the borehole surface are known as compressional head waves. The critical incidence angle θi=sin−1(Vf/Vc) where Vf is the compressional wave speed in the borehole fluid; and Vc is the compressional wave speed in the formation. As the compressional head wave travels along the interface, it radiates energy back into the fluid that can be detected by the hydrophone receivers placed in the fluid-filled borehole. In fast formations, the shear head wave can be similarly excited by a compressional wave at the critical incidence angle θi=sin−1(Vf/Vs), where Vs is the shear wave speed in the formation. It is also worth noting that head waves are excited only when the wavelength of the incident wave is smaller than the borehole diameter so that the boundary can be effectively treated as a planar interface.
In a homogeneous and isotropic model of fast formations, as above noted, compressional and shear head waves can be generated by a monopole source placed in a fluid-filled borehole for determining the formation compressional and shear wave speeds. It is known that refracted shear head waves cannot be detected in slow formations (where the shear wave velocity is less than the borehole-fluid compressional velocity) with hydrophone receivers placed in the borehole fluid. In slow formations, formation shear velocities are obtained from the low-frequency asymptote of the flexural dispersion. There are standard processing techniques for the estimation of formation shear velocities in either fast or slow formations from an array of recorded dipole waveforms.
Recorded waveforms at an array of hydrophone receivers can be processed by a modified matrix pencil algorithm to isolate both non-dispersive and dispersive arrivals in the wavetrain. Slowness dispersions in a fluid-filled borehole (with or without tool) can also be calculated from the solution of a classical boundary-value problem. To calculate dispersions, one or more of the following geometrical and material parameters of the equivalent tool structure, borehole fluid, casing pipe and formation can be used: (1) Surface impedance condition at the boundary between the tool and borehole fluid or equivalent tool model parameters and tool size (when necessary), (2) borehole fluid compressional velocity and mass density, (3) casing pipe inner and outer radii, mass density, compressional and shear velocities, and (4) formation mass density, compressional and assumed shear velocities.
Sanding can occur anytime in unconsolidated sandstone reservoir. Severe sand production can seriously damage a well, reduce the production or disable surface equipment. Therefore, it is desirable to develop reliable technologies to identify zones or depths which are more susceptible to sand production.